# Representing Linear and Exponential Growth

## Mathematical goals

This lesson unit is intended to help you assess how well students are able to interpret exponential and linear functions and in particular, to identify and help students who have the following difficulties:

- Translating between descriptive, algebraic, tabular, and graphical representation of the functions.
- Recognizing how and why a quantity changes per unit interval.

To achieve these goals students work on simple and compound interest problems.

## Introduction

The lesson unit is structured in the following way:

- Before the lesson, students work individually on an assessment task designed to reveal their current understanding and difficulties working with linear and exponential functions. You review their responses and create questions for students to consider, to help them improve their work.
- After a whole-class interactive introduction, students work in small groups on a series of collaborative card matching tasks.
- In a whole-class discussion, students review the main mathematical concepts of the lesson and the strategies used.
- Students then return to the original task, consider their own responses and the questions posed and use what they have learned to complete a similar task.

## Materials required

- Each student will need a copy of the assessment tasks
*Making Money?*and*Making Money?(revisited),*a calculator, a mini-whiteboard, a pen, and an eraser. - Each small group of students will need cut-up copies of
*Card Set: Investment Plans and Formulas, Card Set: Graphs*,*Card Set: Tables*, and*Card Set: Statements*, a large sheet of poster paper, a marker, and a glue stick. - There is a projector resource to help introduce activities and support whole-class discussion.

## Time needed

20 minutes before the lesson, a 100-minute lesson (or two 55-minute lessons), and 20 minutes in a follow-up lesson. Timings are approximate. Exact timings will depend on the needs of your class.

## Lesson Type

## Mathematical Practices

This lesson involves a range of *mathematical practices* from the standards, with emphasis on:

- MP1: Make sense of problems and persevere in solving them
- MP2: Reason abstractly and quantitatively
- MP4: Model with mathematics
- MP5: Use appropriate tools strategically
- MP7: Look for and make use of structure
- MP8: Look for and express regularity in repeated reasoning

## Mathematical Content Standards

This lesson asks students to select and apply mathematical content from across the grades, including the *content standards:*

- H.A-SSE: Interpret the structure of expressions
- H.A-SSE: Write expressions in equivalent forms to solve problems
- H.F-BF: Build a function that models a relationship between two quantities
- H.F-LE: Construct and compare linear and exponential models and solve problems
- H.F-LE: Interpret expressions for functions in terms of the situation they model